Course
Doctorate Degree
Research title
Category, Fixed Point and Information
Research abstract
Our objective with this research is to study the concept of information and fixed point under
the point of view of category theory. Specifically, information is thought as Kolmogorov
complexity. With the analysis of this concept we want to study the Lawvere fixed point theorem,
trying to identify if Chaitin incompleteness theorem and other paradoxical results that apparently
don’t use the fixed point theorem may be thought as an application or not of the Lawvere fixed point. In conjunction to that, we are interested in investigate how the concept of randomness,
defined by the concept of complexity, by the the way Martin-Löf described or by martingales, may
be thought by the optic of category theory.
Graduate Advisor
Edelcio Gonçalves de Souza
Lattes (curriculum vitae)
Funding
CNPq